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When do improved covariance matrix estimators enhance portfolio optimization? An empirical comparative study of nine estimators

The use of improved covariance matrix estimators as an alternative to the sample estimator is considered an important approach for enhancing portfolio optimization. Here we empirically compare the performance of 9 improved covariance estimation procedures by using daily returns of 90 highly capitalized US stocks for the period 1997-2007. We find that the usefulness of covariance matrix estimators strongly depends on the ratio between estimation period T and number of stocks N, on the presence or absence of short selling, and on the performance metric considered. When short selling is allowed, several estimation methods achieve a realized risk that is significantly smaller than the one obtained with the sample covariance method. This is particularly true when T/N is close to one. Moreover many estimators reduce the fraction of negative portfolio weights, while little improvement is achieved in the degree of diversification. On the contrary when short selling is not allowed and T>N, the considered methods are unable to outperform the sample covariance in terms of realized risk but can give much more diversified portfolios than the one obtained with the sample covariance. When T<N the use of the sample covariance matrix and of the pseudoinverse gives portfolios with very poor performance.